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            <h1>初中数学必须掌握的有理数基础知识</h1>
            <div>
              <span>2022-10-06</span>
              <span>156人浏览</span>
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              <p><img src="../assets/imgs/数学3.jpg" alt="" width="700" /></p>
              <p>1、0既不是正数,也不是负数、</p>
              <p>2、正整数、零和负整数统称为整数、</p>
              <p>3、整数和分数统称为有理数、</p>
              <p>4、零和正整数称为自然数、</p>
              <p>5、0和正数统称为非负数: 0和负数统称为非正数、</p>
              <p>6、规定了原点、单位长度和正方向的直线叫做数轴、</p>
              <p>7、在数轴上表示的两个数,右边的数总比左边的数大。</p>
              <p>8、正数都大于零,负数都小于零,正数大于负数、</p>
              <p>9、最小的正整数是1最 大的负整数是-1</p>
              <p>10、只有符号不同的两个数称互为相反数、</p>
              <p>11、相反数等于它本身的数是0、</p>
              <p>12、a的相反数记作-a。</p>
              <p>
                13、负数的相反数大于它本身;
                0的相反数等于它本身;正数的相反数小于它本身
              </p>
              <p>14、若a,b互为相反数，则a+b=0、 a/b=-1&nbsp;</p>
              <p>
                15、我们把在数轴上表示a的点与原点的距离叫做a的绝对值,记作 lal
              </p>
              <p>16、绝对值等于它本身的数是 0和正数</p>
              <p>17、负数的绝对值是它的相反数</p>
              <p>18、对于任意有理数a、总有|a|≥0;a²≥o、</p>
              <p>19、数轴上表示互为相反数的两个点到原点的距离相等、</p>
              <p>20、|a|=a(a≥0)&nbsp; &nbsp;|a|=-a(a≤0)</p>
              <p>21、两个负数,绝对值大的反而小 。</p>
              <p>22、有理数的加法法则:</p>
              <p>(1)同号两数相加，取与加效相同的符号,井把绝对值相加;</p>
              <p>
                (2)绝对值不相等的异号两数相加,取绝对值较大的加数的符号、井用较大的绝对值减去较小的绝对值:
              </p>
              <p>(3)互为相反数的两个数相加得0 ; 、</p>
              <p>(4) -个数与零相加，仍得这个数、</p>
              <p>23、有理数的加法满足交换律和结合律:</p>
              <p>加法交换律:两个 数相加，交换加数的位置，和不变</p>
              <p>a+b=b+a</p>
              <p>
                加法结合律:三个数相加、先把前两个数相加、或者先把后两个数相加，和不变、
              </p>
              <p>(a+b)+c=a+(b+c)</p>
              <p>24、有理数的减法法则:减去- 一个数, 等于加上这个数的相反数、</p>
              <p>25、有理数的乘法法则:</p>
              <p>两数相乘,同号得正,异号得负,并把绝对值相乘、</p>
              <p>任何数与0相乘、都得0 、</p>
              <p>
                任何数与1相乘,积是这个数,任何数与( -1)
                相乘，积是这个数的相反数、
              </p>
              <p>26、有理数的乘法满足交换律和结合律:</p>
              <p>乘法交换律:两个数相乘, 交换因数的位置,积不变、</p>
              <p>ab= ba</p>
              <p>
                乘法结合律:三个数相乘,先把前两个数相乘,或者先把后两个数相乘，积不变、
              </p>
              <p>(ab)c = a(bc)</p>
              <p>
                27、多个有理数相乘、
                -般地、我们有:几个不等于零的数相乘,积的正负号由负因数的个数决定,当负因数的个数为奇数时，积为负;当负因数的个数为偶数时,积为正、
                (奇负偶正)几个数相乘，有一-个数为零,积就为0。
              </p>
              <p>28、若abc&gt;0,a&lt;0,且ac&lt;0,则b&lt;0,c&gt; 0、</p>
              <p>29、若a,b互为倒数,则ab=1</p>
              <p>30、0没有倒数; 倒数等于它本身的数是1和-1、 、</p>
              <p>
                32、有理数的除法可以转化为乘法:除以-
                -个数、等于乘以这个数的倒数、
              </p>
              <p>33、有理数的除法法则: 、</p>
              <p>两数相除，得正，异号得负,并把绝对值相除</p>
              <p>
                34、求几个相同因数的积的运算,叫做乘方,乘方的结果叫做幂、在a”中、
                a叫做底数、 n叫做指数、 a”读作幂。
              </p>
              <p>35、(-6)²的底数是-6、-6²的底数是6</p>
              <p>(-6)²=36、 -6²=-36、 -(-3)²= -9</p>
              <p>36、当负数和分数作底数时、底数应加小括号、</p>
              <p>
                37、正数的任何次幂都是正数;负
                数的奇次幂是负数,负数的偶次幂是正数
              </p>
              <p>39、(- 1)的奇次幂等于-1、 (- 1)的偶次幂等于1</p>
              <p>40、若几个非负数的和为0,则每个非负数分别等于0</p>
              <p>41、若(a-1)²+(B- 2)²=0,则a=1 ,b=2、</p>
              <p>42、若(a-1)*+(b-2)*=0,</p>
              <p>则a=1_ ,b=2_ 、</p>
              <p>
                44、-个大于10 的数、可以记成ax 10"的形式，其中a满足1≤a≤10,
                n是正整数,像这样的记数法叫做科学记数法、
              </p>
              <p>45、有理数的混合运算,应按以下顺序进行:</p>
              <p>(1)先算乘方,再算乘除,最后算加减;</p>
              <p>(2)同级运算,按照从左到右的顺序进行;</p>
              <p>
                (3)如果有括号、就先算小括号里的、再算中括号里的、然后算大括号里的、注意:进行分数的乘除运算时,一般要把带分数化为
              </p>
              <p>假分数、把除法转化为乘法、</p>
              <p>46、若|m|=|n|则m,n的关系是m=±n</p>
              <p>附加:</p>
              <p>|A-B|=A-B(A≥B)&nbsp; &nbsp; |A-B|=B-A(A≤B)</p>
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